Solve the given initial-value problem. y(x) = 5y"+y' = -4x, y(0) = 0, y'(0) = -20

Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

A:

Q: Solve the equation y''' - y'' - 2y'= 0

A:

Q: trmd the equation of the bisectors of the angles between the planes -22 3 32 22-y +²2² +²³ J 2-3y…

A:

Q: Find the general solution by undetermined coefficients.  y'' + y = 2x2e-x.

A:

Q: Find the solution to the equation y' - y = x2y2

A:

Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

A:

Q: y' = 3x²+y² xy ; given that y(1) = 1 ; solve for y when x = 2

A: The given equation is; y'=(3x2+y2)/xy, y(1)=1.

Q: 3. Solve each equation. y(0) = 1, y' (0) = -1 (a) y" + 4y = 0, (b) y" + 5y = 0

A: We have to solve given problem:

Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

A:

Q: 2yy" = 1 + (y')² 2

A:

Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: The general solution of y' = 10 can be written in the form Y =C D

A: We are solving the given problem by using the method of separation of variable.

Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: Solve for y in two ways. y' - 5y = -3

A:

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: .1 Solve the equation x'y"-3xy'+3y 2x'e by method of variation of parameters.

A:

Q: Solve for y. y' = 7x + xy​; y = - 4 when x = 0

A: Given,  y'=7x+xy,  y=-4 when x=0

Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

A:

Q: Use the method of undetermined coefficients to determine the form of a particular solution to the…

A:

Q: Solve  y'' − 2y' + 5y = x2 + 1

A: Solution

Q: Solve the IVP. (35 53 X' = X with X(0) = - (4).

A:

Q: reduce to linear form and solve the following equation y'+(1/2x)y=x/(y^3)  y(1)=2

A: The given differential equation is: y'+12xy=xy3  …1,   y1=2 This is Bernoulli's equation,so (1) can…

Q: 4. Solve (x-2)y" - (4x-7)y' + (4x-6)y= 0, if y₁ = e2x is one known solution? HO The Cystem 2e²t

A:

Q: Find the general solution by Variation of Parameters. y''+y=3cscx

A: